Question

A triangle has sides of length 11 cm and 5 cm. What can you say about the length of the third​ side?

Answer 1

Based on the given information, we can use the triangle inequality theorem to determine the range of possible lengths for the third side of the triangle. The theorem states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's consider the two given side lengths:
11 cm + 5 cm = 16 cm

Therefore, the sum of the lengths of the two given sides is 16 cm.

According to the triangle inequality theorem, the length of the third side must be greater than the difference between the sum of the lengths of the two given sides and the length of the longer side, and less than the sum of the lengths of the two given sides.

The longer side length is 11 cm, so:
16 cm - 11 cm < Length of third side < 16 cm + 11 cm
5 cm < Length of third side < 27 cm

Therefore, the length of the third side can be any value between 5 cm and 27 cm (exclusive).